Variational Analysis in Sobolev and BV Spaces

Hedy Attouch is a professor in the Institut de Mathématique et de Modélisation de Montpellier II, where he also has been director of the Laboratory of Convex Analysis and of ACSIOM. His research focuses on variational analysis, convex analysis, continuous optimization, semialgebraic optimization, gradient flows, the interaction among these fields of research, and their applications. He has published more than 100 articles in international journals and has written six books. He serves as editor for several journals on continuous optimization and is responsible for several international research programs. Giuseppe Buttazzo is a professor in the Department of Mathematics at the University of Pisa. He has been a keynote speaker at many international conferences and workshops on the fields of calculus of variations, nonlinear PDEs, applied mathematics, control theory and related topics. He is the author of more than 180 scientific publications and 20 books, and he serves as an editor of several international journals. Gérard Michaille is a professor at the University of Nîmes and member of the UMR-CNRS Institut de Mathématique et de Modélisation de Montpellier. He works in the areas of variational analysis, homogenization, and the applications of PDEs in mechanics and physics.

Preface to the second edition; Preface to the first edition; 1. Introduction; Part I. Basic Variational Principles: 2. Weak solution methods in variational analysis; 3. Abstract variational principles; 4. Complements on measure theory; 5. Sobolev spaces; 6. Variational problems: some classical examples; 7. The finite element method; 8. Spectral analysis of the Laplacian; 9. Convex duality and optimization; Part II. Advanced Variational Analysis: 10. Spaces BV and SBV; 11. Relaxation in Sobolev, BV, and Young measure spaces; 12. Γ-Convergence and applications; 13. Integral functionals of the calculus of variations; 14. Applications in mechanics and computer vision; 15. Variational problems with a lack of coercivity; 16. An introduction to shape optimization problems; 17. Gradient flows; Bibliography; Index.